POWER POINT PRESENTATIONS

Introduction to Scientific Computing

• • • Introduction to numerical methods [PDF] [PPT] [MORE]
    • Measuring errors [PDF] [PPT] [MORE]
    • Sources of error [PDF] [PPT] [MORE]
    • Binary representation of numbers [PDF] [PPT] [MORE]
    • Floating point representation of numbers [PDF] [PPT] [MORE]
    • Propagation of errors [PDF] [PPT] [MORE]
    • Taylor series [PDF] [PPT] [MORE]

Differentiation

• • • Continuous functions [PDF] [PPT] [MORE]
    • Discrete functions [PDF] [PPT] [MORE]
    • Effect of step size on accuracy of numerical first derivative: Forward Divided Difference [PDF] [PPT]
    • Effect of step size on accuracy of numerical first derivative Backward Divided Difference [PDF] [PPT]
    • Effect of step size on accuracy of numerical first derivative: Central Divided Difference [PDF] [PPT]

Nonlinear Equations

• • • Bisection Method [PDF] [PPT] [MORE]
    • Newton-Raphson Method [PDF] [PPT] [MORE]
    • Secant Method [PDF] [PPT] [MORE]

Simultaneous Linear Equations

• • • Gaussian Elimination [PDF] [PPT] [MORE]
    • LU Decomposition method [PDF] [PPT] [MORE]
    • Gauss-Seidel method [PDF] [PPT] [MORE]

Interpolation

• • • Direct Method [PDF] [PPT] [MORE]
    • Newton’s Divided Difference Method [PDF] [PPT] [MORE]
    • Lagrange Method [PDF] [PPT] [MORE]
    • Spline Method [PDF] [PPT] [MORE]

Regression

• • • Linear Regression [PDF] [PPT] [MORE]
    • Nonlinear regression [PDF] [PPT] [MORE]

Integration

• • • Trapezoidal Rule [PDF] [PPT] [MORE]
    • Simpson’s 1/3rd Rule [PDF] [PPT] [MORE]
    • Romberg Rule [PDF] [PPT] [MORE]
    • Gauss-Quadrature Rule [PDF] [PPT] [MORE]

Ordinary Differential Equations

• • • Euler’s Method [PDF] [PPT] [MORE]
    • Runge-Kutta 2nd order Method [PDF] [PPT] [MORE]
    • Runge-Kutta 4th order Method [PDF] [PPT] [MORE]
    • Shooting Method [PDF] [PPT] [MORE]
    • Finite Difference Method [PDF] [PPT] [MORE]

Optimization

• • • Golden Section Search Method [PDF] [PPT] [MORE]
    • Newton’s Method [PDF] [PPT] [MORE]
    • Multidimensional Direct Search Method [PDF] [PPT] [MORE]
    • Multidimensional Gradient Method [PDF] [PPT] [MORE]

Partial Differential Equations

• • • Introduction to Partial Differential Equations [PDF] [PPT] [MORE]
    • Parabolic Partial Differential Equations [PDF] [PPT] [MORE]
    • Elliptic Partial Differential Equations [PDF] [PPT] [MORE]

Fast Fourier Transforms

• • • Introduction to Fourier Series [PDF] [PPT] [MORE]
    • Continuous Fourier Series [PDF] [PPT] [MORE]
    • Fourier Transform Pair [PDF] [PPT] [MORE]
    • Discrete Fourier Transform [PDF] [PPT] [MORE]
    • Informal Development of Fast Fourier Transform [PDF] [PPT] [MORE]